The present invention relates generally to forming a bubble in liquid, and, more particularly, to a method for determining the optimum pressure for forming a bubble in a liquid.
There are many technologies that make use of the ability to form and maintain a bubble in a liquid. For example, devices using bubbles have been used as valves, pumps, switches, and other functions. The formation of a bubble causes nearby liquid to move. The liquid motion may be used to actuate a mechanism such as changing the state of a fluidic valve, pushing on a mechanical switch, changing the reading on a pressure sensor, or the like. Alternatively, the bubble itself may be used to block fluid motion, as part of a display, or a region of low refractive index for control of optical functions (e.g., to block or reflect a beam of light).
Generally, a bubble is formed in a liquid by heating the liquid using an adjacent hot surface, although other means (light, electrical current, microwave) can be employed. Since it is difficult to confine heating to a small spatial region, a portion of the applied heat goes to heating adjacent material such as support structures, electrical conductors, and the like. It is customary to form bubbles in these systems at pressures equal to or close to atmospheric pressure. Unfortunately, at pressure close to atmospheric pressure a relatively high temperature is required to boil the liquid and form the bubble. At this relatively high temperature, the heat lost to the surrounding support structures may prove excessive for the system.
When a bubble is created at a sub-atmospheric pressure, the bubble is formed at a lower temperature than when formed at atmospheric pressure, leading to lower heat loss. However, creating a bubble in a liquid at a lower temperature also increases the heat of vaporization per mole and the work that must be performed against the surface tension required to create the bubble compared with creating the bubble at a higher temperature. Therefore, it would be desirable to have a way to determine whether it is beneficial to form a bubble in a liquid at pressures below atmospheric pressure, which will reduce the temperature at which the bubble forms.
The invention provides a method by which to accurately determine the optimum pressure with which to operate a device in which a bubble is formed within a container.
The present invention may be conceptualized as a method for determining optimum ambient pressure that minimizes the energy required to form a bubble of a given volume in a liquid, the method comprising the following steps: entering a first pressure and a second pressure; calculating a first boiling temperature corresponding to the first pressure; calculating a second boiling temperature corresponding to the second pressure; entering a surface tension of the bubble at the first boiling temperature and the second boiling temperature; entering a heat of vaporization (Hv) value of the liquid at the first boiling temperature and the second boiling temperature; calculating a first energy required to vaporize the liquid at the first pressure; calculating a second energy required to vaporize the liquid at the second pressure; determining whether the first energy required at the first pressure is greater than the second energy required at the second pressure; and forming the bubble at the pressure corresponding to the lower of the first energy or the second energy.
The invention has numerous advantages, a few of which are delineated, hereafter, as merely examples.
An advantage of the invention is that it allows a bubble to be formed within a container using the lowest possible pressure, and therefore, at the lowest possible temperature.
Another advantage of the invention is that it allows for the rapid formation of a bubble in a liquid.
Another advantage of the invention is that it allows for the accurate determination of the optimal system pressure in a bubble-actuated device.
Another advantage of the invention is that it minimizes the energy required to form a bubble in a given liquid and in a given geometry.
Other features and advantages of the invention will become apparent to one with skill in the art upon examination of the following drawings and detailed description. These additional features and advantages are intended to be included herein within the scope of the present invention.